Instantons, fluctuations and singularities in the supercritical stochastic nonlinear Schroedinger equation
arxiv(2024)
摘要
Recently, Josserand et al. proposed a stochastic nonlinear Schroedinger model
for finite-time singularity-mediated turbulence [Phys. Rev. Fluids 5, 054607
(2020)]. Here, we use instanton calculus to quantify the effect of extreme
fluctuations on the statistics of the energy dissipation rate. While the
contribution of the instanton alone is insufficient, we obtain excellent
agreement with direct simulations when including Gaussian fluctuations and the
corresponding zero mode. Fluctuations are crucial to obtain the correct scaling
when quasi-singular events govern the turbulence statistics.
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